Enhanced Euclid Algorithm for Modular Multiplicative Inverse and Its Application in Cryptographic Protocols
Boris S. Verkhovsky
DOI: 10.4236/ijcns.2010.312123   PDF    HTML     6,602 Downloads   11,955 Views   Citations


Numerous cryptographic algorithms (ElGamal, Rabin, RSA, NTRU etc) require multiple computations of modulo multiplicative inverses. This paper describes and validates a new algorithm, called the Enhanced Euclid Algorithm, for modular multiplicative inverse (MMI). Analysis of the proposed algorithm shows that it is more efficient than the Extended Euclid algorithm (XEA). In addition, if a MMI does not exist, then it is not necessary to use the Backtracking procedure in the proposed algorithm; this case requires fewer operations on every step (divisions, multiplications, additions, assignments and push operations on stack), than the XEA. Overall, XEA uses more multiplications, additions, assignments and twice as many variables than the proposed algorithm.

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B. Verkhovsky, "Enhanced Euclid Algorithm for Modular Multiplicative Inverse and Its Application in Cryptographic Protocols," International Journal of Communications, Network and System Sciences, Vol. 3 No. 12, 2010, pp. 901-906. doi: 10.4236/ijcns.2010.312123.

Conflicts of Interest

The authors declare no conflicts of interest.


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